Two-layer optimal collision-avoidance enclosing control for multiple satellites against an escaping target under incomplete information condition and sensor faults

Problem of collision-free target-enclosing (TE) control by a group of weak-maneuverability service satellites (SSats) against a noncooperative target satellite (TSat) whose dynamics and escaping behavior are fully unknown is studied in this paper. A two-layer prescribed-performance optimal cooperative target-enclosing (POCT) controller is proposed. To reduce the running load and measuring requirements of the low-cost SSats, by appointing a leader satellite (LSat), a decoupling mechanism is proposed, and it is proved to equivalently divide the studied TE task into two layers, including information-incomplete target pursuit (TP) layer and collision-free configuration tracking (CT) layer. In the inner TP layer, to overcome the challenges caused by the escaping unknown TSat under sensor faults, initial-condition-free boundaries are proposed which can directly constrain the TP error to perform prescribed transient and steady-state behaviors, and then the TP controller can be constructed with only using measurement data with sensor faults. Meanwhile, in the external CT layer, by describing the collision-free CT issue as a nonlinear nonzero-sum differential game and introducing an auxiliary variable into the Nash equilibrium approximation error, a high-precision optimal enclosing CT controller with collision avoidance is designed, which guarantees an asymptotical tracking for the desired configuration. The control objectives are proved to be achieved by the proposed POCT controller. Finally, the advantages on infinite initial constraint range, whole-process performance setting achieved by the inner layer design and better CT performance achieved by the external layer design are shown through simulation results.